Conventional sliding gears of speed-changing transmissions, having straight clutch teeth on an end face, are mainly used for shifting into reverse. For reasons of convenience in cases where the driving member is a jack shaft, even in transmissions with otherwise obliquely toothed gears, the idler gear of the first forward speed ratio also has straight (i.e. axially extending) teeth. If, in order to obtain a larger number of forward speed ratios, a main or basic transmission unit is connected in cascade with a range or group transmission unit so that the first speed ratio is also used, for example, as a 5th ratio, it is convenient for various reasons to provide the first-ratio and reverse gears also with inclined teeth. On account of the relatively high axial forces in the case of inclined running teeth, it is a very expensive matter to lock the sliding gear in such transmissions. The generally practiced back-angling of the clutch teeth must give rise to a considerable restraining force, which is achieved to the detriment of ready shiftability. Moreover, this solution is not reliable in at least one loading direction (pulling or pushing), so that such relatively simple sliding gears are not normally utilized. Obliquely toothed gears of the kind specified are therefore mounted rotatable but axially fixed on the output shaft, for example, and gear shifting is performed via a sliding sleeve by engagement of a coupling member with the clutch teeth of such gears. This arrangement is substantially more expensive to construct and less compact in the axial direction.